A Stochastic and Dynamic Vehicle Routing Problem with Time Windows and Customer Impatience

In this paper, we study the problem of designing motion strategies for a team of mobile agents, required to fulfill request for on-site service in a given planar region. In our model, each service request is generated by a spatio-temporal stochastic process; once a service request has been generated, it remains active for a certain deterministic amount of time, and then expires. An active service request is fulfilled when one of the mobile agents visits the location of the request. Specific problems we investigate are the following: what is the minimum number of mobile agents needed to ensure that a certain fraction of service requests is fulfilled before expiration? What strategy should they use to ensure that this objective is attained? This problem can be viewed as the stochastic and dynamic version of the well-known vehicle routing problem with time windows. We also extend our analysis to the case in which the time service requests remain active is itself a random variable, describing customer impatience. The customers’ impatience is only known to the mobile agents via prior statistics. In this case, it is desired to minimize the fraction of service requests missed because of impatience. Finally, we show how the routing strategies presented in the paper can be executed in a distributed fashion.     

Queuing network models for delay analysis of multihop wireless ad hoc networks

In this paper we analyze the average end-to-end delay and maximum achievable per-node throughput in random access multihop wireless ad hoc networks with stationary nodes. We present an analytical model that takes into account the number of nodes, the random packet arrival process, the extent of locality of traffic, and the back off and collision avoidance mechanisms of random access MAC. We model random access multihop wireless networks as open G/G/1 queuing networks and use the diffusion approximation in order to evaluate closed form expressions for the average end-to-end delay. The mean service time of nodes is evaluated and used to obtain the maximum achievable per-node throughput. The analytical results obtained here from the queuing network analysis are discussed with regard to similarities and differences from the well established information-theoretic results on throughput and delay scaling laws in ad hoc networks. We also investigate the extent of deviation of delay and throughput in a real world network from the analytical results presented in this paper. We conduct extensive simulations in order to verify the analytical results and also compare them against NS-2 simulations.     

Stochastic Event Capture Using Mobile Sensors Subject to a Quality Metric

Mobile sensors cover more area over a fixed period of time than do the same number of stationary sensors. However, the quality of coverage (QoC) achieved by mobile sensors depends on the velocity, mobility pattern, number of mobile sensors deployed, and the dynamics of the phenomenon being sensed. The gains attained by mobile sensors over static sensors and the optimal motion strategies for mobile sensors are not well understood. In this paper, we consider the following event capture problem: the events of interest arrive at certain points in the sensor field and disappear according to known arrival and departure time distributions. An event is said to be captured if it is sensed by one of the mobile sensors before it fades away. We analyze how the QoC scales with velocity, path, and number of mobile sensors. We characterize cases where the deployment of mobile sensors has no advantage over static sensors, and find the optimal velocity pattern that a mobile sensor should adopt. We also present algorithms for two motion planning problems: 1) for a single sensor, what is the sensor trajectory and the minimum speed required to satisfy a bound on the event loss probability and 2) for sensors with fixed speed, what is the minimum number of sensors required to satisfy a bound on the event loss probability. When the robots are restricted to move along a line or a closed curve, our algorithms return the optimal velocity for the minimum velocity problem. For the minimum sensor problem, the number of sensors used is within a factor of 2 of the optimal solution. For the case where the events occur at arbitrary points on a plane, we present heuristic algorithms for the aforementioned motion planning problems and bound their performance with respect to the optimal.